If √ x + √ y = 11 and y ( 4 ) = 81, find y ' ( 4 ) by implicit differentiation.

Answer 1

(1/2)/sqrx + (1/2)/sqry(y') = 0

1/sqrx + 1/sqry(y') = 0

y' = -sqr(y/x)

y'(4) =- sqr(81/4) = -9/2

or solve the original equation for y and take the derivative

sqry = 11- sqrx

y = 121 - 22sqrx + x

y' = -11/sqrx + 1

y'(4) = -11/2 + 1 = -9/2